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Feb. 11, 2019, 9:01 PM GMT / Updated Feb. 12, 2019, 5:04 AM GMT

By Lauren Egan and Dareh Gregorian

EL PASO, Texas — President Donald Trump and Beto O'Rourke faced off less than half a mile — but worlds apart — from each other on Monday night.

"A young man who’s got very little going for himself except he’s got a great first name," Trump said of O'Rourke, a former congressman from El Paso and potential 2020 Democratic presidential candidate, and dubbed O'Rourke's rivaling event crowd size as "not too good."

"That may be the end of his presidential bid," Trump opined.

The president's trip to El Paso was designed to rally public support for his call for a wall along the southern border. Democrats have refused his demand for $5.7 billion in funding for the wall, which Trump had said during the 2016 presidential campaign that Mexico would pay for. Without a deal, the government could close again after Friday when the current spending deal expires.

But shortly before Trump spoke in El Paso, bipartisan negotiators in Washington announced that they had reached the outlines of a possible deal on border security that could head off another shutdown.

"They said that progress is being made with this committee," Trump told the crowd. "Just so you know, we’re building the wall anyway."

"Walls work," he added, speaking in front of two large banners that read “Finish The Wall."

Down the street from Trump, O'Rourke had a very different message to send.

El Paso is "one of the safest cities in the United States of America," O'Rourke said at the "March for Truth: Stop the Wall, Stop the Lies" rally. "Safe, not because of walls — but in spite of walls."

"Walls do not save lives. They end lives," O'Rourke added, taking a direct jab at Trump's messaging.

The fighting began hours before the dueling events got underway.

"We have a line that is very long already," Trump told reporters in Washington before departing for Texas, referring to people waiting to get into his campaign rally. "And I understand our competitor's got a line too, but it's a tiny little line."

Tension between Trump and the El Paso community had sparked even earlier, when the president used the city to call for a barrier on the southern border during his State of the Union address.

"The border city of El Paso, Texas, used to have extremely high rates of violent crime — one of the highest in the country, and considered one of our nation's most dangerous cities," Trump falsely claimed during his address. “Now, with a powerful barrier in place, El Paso is one of our safest cities."

Trump's claims about the border town led to bipartisan pushback from El Paso politicians, who have pointed to statistics that the city of 700,000 was never one of the country's most dangerous — and it had already transformed itself into one of the safest by the time wall was built.

"El Paso was NEVER one of the MOST dangerous cities in the US. We‘ve had a fence for 10 years and it has impacted illegal immigration and curbed criminal activity. It is NOT the sole deterrent. Law enforcement in our community continues to keep us safe," Mayor Dee Margo, a Republican, tweeted after the State of the Union.

El Paso was NEVER one of the MOST dangerous cities in the US. We‘ve had a fence for 10 years and it has impacted illegal immigration and curbed criminal activity. It is NOT the sole deterrent. Law enforcement in our community continues to keep us safe #SOTU

The county commissioners passed a resolution on Monday complaining that Trump had "continuously made inaccurate claims about the United States' southern border, including El Paso," and saying they're "disillusioned by President Trump's lies regarding the border and our community."

Trump pushed back Monday night. “I don’t care if they’re a Republican or a Democrat, they are full of crap when they say it [the border wall] hasn’t made a big difference,” he said.

Violent crime in El Paso peaked in 1993, but has been cut in half since, reaching its lowest point in 2006, before the wall was built.

There were 19 murders and 1,819 aggravated assaults in the city in 2017, according to FBI crime data. The murder rate is about half that of the national average.

Tonight, we will meet lies and hate with the truth and a positive, inclusive, ambitious vision for the future from the U.S.-Mexico border. Join us:️5:00 march at Bowie HS️6:00 celebration of El Paso at Chalio Acosta Park

Just ahead of the Trump's rally, O'Rourke dismissed the president's continued claims about the border town.

"Nobody tells our story better than we do," O'Rourke told NBC News in El Paso. "It’s incredibly important that this community stand up to be counted, to tell the story and to make sure that we set the record straight. That this is, as you know, a march for truth...we are here to follow the lead of this great community and make sure the country sees us at our best."

Asked how he'd respond if the president called him names at his Monday night event, O'Rourke laughed. "I really don’t care about that," he said.

On their Facebook page for the march against the wall, organizers urged attendees to "Wear white," "Try to carpool or use rideshare," and "Bring a positive poster."

The march proceeded along a section of fencing before ending in a rally at the Chalio Acosta Sports Center, less than half a mile from the El Paso County Coliseum, where Trump spoke.

Pro-Trump vendors were set up across the street Monday morning from where O'Rourke was to speak, but the area isn't big Trump country. Trump won Texas by nine points in the 2016 election, but he lost El Paso County by 43 points — 69 percent to 26 percent.

O'Rourke tweeted ahead of the event that participants would "meet lies and hate with the truth and a positive, inclusive, ambitious vision for the future."